Discusses critical thinking as the process of moving fluently among abstraction levels. Defines three components involved in fluency of movement: (1) knowledge, or an awareness of the existence of abstraction levels; (2) payoff, or the reason for acquiring fluency; and (3) timing, or a consciousness of abstraction levels at a given time and place.…

According to Humean framework, relations are judged to be causal to extent that they are characterized by regularity, continuity, and covariation among college students and college-bound 11- and 14-year-olds. Presents subjects with information about one of the following indices: potential causal factor covaried with effect and potential causal…

Research by Labov dealing with everyday speech and its relation to thinking and reasoning is critiqued, and Cooper's detailed criticism of Labov's research is discussed. Researchers should pay attention to actual speech in settings that are natural, rather than using only quantitative abstractions from artificial and restricted verbal encounters.…

Contrasts artificial behavior with artificial intelligence, traces Law of Effect's development from a verbal statement into a mathematical model providing algorithms for artificial behavior programs, and describes an attempt to use computer graphics and animation to simulate behavior and teach abstract concepts. (MBR)

Suggests having students write short summaries using the principles of the journalistic news "lead" to help them sharpen their abstraction skills. Includes samples of data blocks from which students would compose their summaries, kernel sentences from the samples, "kernel" kernel sentences, first draft summaries, and 30-word…

Discusses students' inability to make the connection between manipulative materials and pencil-and-paper calculations in mathematics instruction. Outlines the development of mathematical ideas through the concrete, representational, and abstract phases of instruction. An annotated bibliography listing teacher resources for representational-level…

Argues that the best way to cultivate children's reasoning is to make philosophy an essential part of the elementary school curriculum. Philosophy alone provides the logical criteria for distinguishing better thinking from poorer. The author's "Philosophy for Children" program is described. (TE)

Reports on research examining the effect of linguistic presupposition on the solving of three-term series problems. (Author/RM)

Children's understanding of Euclidian space was investigated using three Piaget-type tasks to examine the ability of children to quantitatively locate a point in one, two, and three dimensions. Among the findings were that a disagreement exists between Piaget's data and the results of this study. (BT)

This paper discusses ways to use worked examples in teaching mathematics. It is argued that neither investigative teaching such as discovery learning nor lecturing and starting from the abstract are helpful as they are based on emotive associations with general labels rather than precise details of pedagogic strategies. (KHR)

This paper reports results related to the development of a consistent descriptive language for research on mathematical reasoning. Ways of reasoning deductively are highlighted, using examples drawn from observations of young students. One-step deductions versus multi-step deductions, known versus hypothetical premises, and single versus multiple…

This research evaluates the effectiveness of computer-mediated support for students' individual and collaborative argumentation. "Convince Me" is a "reasoner's workbench" program that aids students in generating and analyzing arguments, providing feedback on argument coherence from a general computational model. Laboratory studies indicate that…

A cross-sectional study examined age differences in children's conceptions of early U.S. history. Students in grades 2, 3, 6, and 8 (n=281) were asked to respond to a question about how the United States became a country. Their essays show significant changes with age. Older students were more likely to include errors of historical fact in their…

Multilevel visual models can make teaching and learning theories more easily understood. The idea of graphic visualizationas developed in this model utilizes three stages of abstract concept formation dealing with concrete visualization, abstract visualization, and abstract generalization, which would provide the learner with an intuitive grasp of…